Related papers: Dynamic Planar Voronoi Diagrams for General Distan…
We study the point location problem on dynamic planar subdivisions that allows insertions and deletions of edges. In our problem, the underlying graph of a subdivision is not necessarily connected. We present a data structure of linear size…
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
Data lakes, increasingly adopted for their ability to store and analyze diverse types of data, commonly use columnar storage formats like Parquet and ORC for handling relational tables. However, these traditional setups fall short when it…
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…
We present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a…
We study metric data structures for curves in doubling spaces, such as trajectories of moving objects in Euclidean $\mathbb{R}^d$, where the distance between two curves is measured using the discrete Fr\'echet distance. We design data…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…
In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance between a point t and a cluster P is the maximum Euclidean distance between t and a point in P. This diagram has direct applications in VLSI design.…
We propose a data structure in $d$-dimensional hyperbolic space that can be considered a natural counterpart to quadtrees in Euclidean spaces. Based on this data structure we propose a so-called L-order for hyperbolic point sets, which is…
Nearest-neighbor search dominates the asymptotic complexity of sampling-based motion planning algorithms and is often addressed with k-d tree data structures. While it is generally believed that the expected complexity of nearest-neighbor…
On-disk graph-based indexes are favored for billion-scale Approximate Nearest Neighbor Search (ANNS) due to their high performance and cost-efficiency. However, existing systems typically rely on a coupled storage architecture that…
Algebraic techniques have had an important impact on graph algorithms so far. Porting them, e.g., the matrix inverse, into the dynamic regime improved best-known bounds for various dynamic graph problems. In this paper, we develop new…
In the nearest neighbor problem, we are given a set $S$ of point sites that we want to store such that we can find the nearest neighbor of a (new) query point efficiently. In the dynamic version of the problem, the goal is to design a data…
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
For a set of $n$ points in the plane, this paper presents simple kinetic data structures (KDS's) for solutions to some fundamental proximity problems, namely, the all nearest neighbors problem, the closest pair problem, and the Euclidean…
This paper presents a simple kinetic data structure for maintaining all the nearest neighbors of a set of $n$ moving points in $\mathbb{R}^d$, where the trajectory of each point is an algebraic function of at most constant degree $s$. The…
In this paper, we propose the DN-tree that is a data structure to build lossy summaries of the frequent data access patterns of the queries in a distributed graph data management system. These compact representations allow us an efficient…